Journal of Magnetism and Magnetic Materials 272–276 (2004) 185–186 Cluster spin glass phase and charge stripe fluctuations in the high-T c superconductor La 2x Sr x CuO 4 F. Cordero a,b, *, A. Paolone b,c , R. Cantelli b,c a CNR, Istituto di Acustica ‘‘O.M. Corbino’’, Roma, Italy b INFM, Italy c Dipartimento di Fisica, Universit " a di Roma ‘‘La Sapienza’’, Roma, Italy Abstract A rise of the acoustic absorption in correspondence with the freezing of the Cu 2þ spins into the cluster spin glass state has been identified with the fluctuations of the walls between the antiferromagnetic spin clusters, pinned by the Sr dopants. The depinning of the stripes is identified with an additional absorption maximum around 80 K; whose intensity and effective activation energy (identified with the pinning barrier) exhibit a dependence on doping consistent with pinning and stripe–strain interaction being mediated by the octahedral tilts. r 2003 Elsevier B.V. All rights reserved. PACS: 74.72.Dn; 62.40.+i; 74.81.g Keywords: Charge stripes; Anelastic spectroscopy; LSCO The conducting CuO 2 planes of the high-T c super- conductors are 2D quantum Heisenberg antiferromag- nets (AF) in the undoped state; by injecting holes, a complex magnetic phase diagram is found. The con- ducting holes segregate into fluctuating stripes, leaving hole-poor domains of Cu 2þ spins with AF correlations. In the underdoped state ðhole density ¼ xo0:1Þ of La 2x Sr x CuO 4 (LSCO), below T g ðxÞC0:2=x K; the spins freeze into a cluster spin glass (CSG) state: each cluster has a direction of the staggered magnetization different from the adjacent clusters, from which is separated by the hole stripes acting as magnetic domain walls [1]. The freezing in the CSG state is accompanied by an increase in the elastic energy loss coefficient, Q 1 ¼ E 00 =E 0 ; where Eðo; T Þ¼ E 0 þ iE 00 is the dynamic elastic modulus [2,3]. This is shown in Fig. 1 for the case x ¼ 0:03 with T g C6:7K: The losses are attributed to the fluctuations of the stripes, which result into fluctuations of the sizes of clusters and finally into strain fluctuations through magnetoelastic coupling. The dependence of the magnitude of the absorption on doping is in agreement with what expected from fluctuations of stripes pinned by the Sr dopants [3]. At higher temperature, the stripes are expected to fluctuate away from the pinning points, overcoming the mean pinning energy E p through thermal activation, with a rate t 1 ¼ t 1 0 expðE p =k B T Þ: In that case, an absorption peak of the form Q 1 ðo; T Þ¼ D ot 1 þðotÞ 2 is expected [4], which allows the rate t 1 to be measured at the peak temperatures T i such that o i t ðT i Þ¼ 1: The frequency is that of the free flexural modes of ceramic samples cut as thin bars B4 cm long; by exciting the higher-frequency modes one measures t 1 at higher values of T i and can deduce the parameters t 0 and E: The relaxation strength DpðDe an Þ 2 =T is determined by the anelastic strain De an involved in the depinning process. Such a process has been identified [5] with an anelastic relaxation maximum occurring at B80 K for a vibration frequency o=2pB1kHz (Fig. 1). Spectra similar to that of Fig. 1 have been measured on a series ARTICLE IN PRESS *Corresponding author. Tel.: +39-06-4993-4114; fax: +39- 06-20660061. E-mail address: cordero@idac.rm.cnr.it (F. Cordero). 0304-8853/$-see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.076